(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

If A, B, C are the interior angles of a triangle ABC, prove that `\tan \frac{B+C}{2}=\cot \frac{A}{2}`

D is a point on the side BC of ∆ABC such that ∠ADC = ∠BAC. Prove that` \frac{"CA"}{"CD"}=\frac{"CB"}{"CA"} or "CA"^2 = "CB" × "CD".`

Solve the equation 4x² – 5x – 3 = 0 and give your answer correct to two decimal places

Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.

The catalogue price of a computer set is Rs. 42,000. The shopkeeper gives a discount of
10% on the listed price. He further gives an off-season discount of 5% on the discounted
price. However, sales tax at 8% is charged on the remaining price after the two successive
discounts. Find

1)the amount of sales tax a customer has to pay

2)the total price to be paid by the customer for the computer set.

P(1, -2) is a point on the line segment A(3, -6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.

How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.

The printed price of an air conditioner is Rs. 45000/-. The wholesaler allows a discount of 10%
to the shopkeeper. The shopkeeper sells the article to the customer at a discount of 5% of the
marked price. Sales tax (under VAT) is charged at the rate of 12% at every stage. Find:

1) VAT paid by the shopkeeper to the government

2) The total amount paid by the customer inclusive of tax.

The mean of following numbers is 68. Find the value of ‘x’. 45, 52, 60, x, 69, 70, 26, 81 and 94. Hence, estimate the median.

The slope of a line joining P(6, k) and Q(1 – 3k, 3) is `1/2`. Find:

1. k.
2. mid-point of PQ, using the value of ‘k’ found in (i).

If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b

Solve the quadratic equation x² –  3(x + 3) = 0; Give your answer correct to two significant figures.

A dealer buys an article at a discount of 30% from the wholesaler, the marked price being Rs. 6000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of the VAT is 6%, find

1) The price paid by the shopkeeper including the tax.

2) The VAT paid by the dealer

If (x + 2) and (x + 3) are factors of x³ + ax + b, find the values of 'a' and `b'.

Solve x² + 7x = 7 and give your answer correct to two decimal places

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series

A man invests Rs. 22,500 in Rs. 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate:

1) The number of shares purchased

2) The annual dividend received.

3) The rate of return he gets on his investment. Give your answer correct to the nearest whole number.

Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of children.

In ΔPQR, MN is parallel to QR and `(PM)/(MQ) = 2/3`

1) Find `(MN)/(QR)`

2) Prove that ΔOMN and ΔORQ are similar.

3) Find, Area of ΔOMN : Area of ΔORQ